| EPSRC Reference: |
GR/S17215/01 |
| Title: |
Invariant Manifolds and Bifurcations in Singular Implicit Systems |
| Principal Investigator: |
Beardmore, Professor RE |
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| Project Partners: |
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| Department: |
Mathematics |
| Organisation: |
Imperial College London |
| Scheme: |
First Grant Scheme Pre-FEC |
| Starts: |
15 March 2004 |
Ends: |
14 December 2006 |
Value (£): |
123,370
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| EPSRC Research Topic Classifications: |
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| EPSRC Industrial Sector Classifications: |
| Energy |
No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The proposed research is to consider novel analytical and numerical aspects of differential-algebraic equations (DAEs) which represent a class of mathematical problems which arise in the physical sciences as models of electrical power networks, in chemical engineering systems, in plantherbivore interactions and constrained mechanics, to name but a few application areas. Although the qualitative properties of solutions of DAEs bear a resemblance to the behaviour observed in the study of differential equations, there are important differences and this proposal is concerned with these. The proposed work will concentrate on two main themes: initial-value problems and boundary-value problems. The first goal (part 1) of the project is to use the Nash-Moser inverse function theorem to prove the result that DAEs can be viewed as differential equations in the vicinity of an equilibrium point, and we then expect (part 2) to obtain similar results for the discrete analogue of DAEs. The second goal of the project (part 3) is to gain an understanding of how an apparent breakdown in the reliability of algorithms for solving boundary-value DAEs occurs. In all cases, possible initial lines of investigation are presented for each problem.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.imperial.ac.uk |